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A design technique, based on the model reference adaptive control approach for the long term ventilation of the lungs is presented. The design objective is to minimize the harmful effects (e.g., interference in the circulatory system, mechanical damage, etc.) due to possible change in the patient's respiratory parameters (i.e., the airway resistance and the lung and chest wall compliance) during the long term ventilation of the lungs. A model, consisting of a fixed resistance capacitance, RC, analog network is used to generate a ``desire'' alveolar pressure profile. The instantaneous difference in the alveolar pressures, obtained from the comparison of the actual patient and his ``desired'' behavior, is fed to an ``adaptive controller.'' The controller, in turn, will adjust the respirator's output pressure (to the patient) in such a way, that the instantaneous difference in alveolar pressure is reduced to zero. The stability of this newly designed adaptive system is ensured by using Lyapunov's direct method in obtaining the updating laws for the adaptive controller. Using a similar design approach, a respiratory parameters identification scheme is introduced. This identification process is able to generate, indirectly, a continuous estimation of the patient's alveolar pressure (which normally is not monitorable in the actual patient) for the purpose of comparison, in this newly designed adaptive system. Digital simulations of the respirator's pressure control and the identification process, as well as the simulation of the combined system, were performed. The result has indeed demonstrated the ability of a speedy performance of this adaptive system.